Question

Question 6 [ 25 points] A father wants to save for his 8-year-old son's college expenses. The son will enter college 10 years from now. An annual amount of $40.000 in constant dollars will be required in order to support the son's college expenses for 4 years. Assume that these college payments will be made at the beginning of the school year. The future general inflation rate is estimated to be 6% per year, and the market interest rate on the savings account will average 8% compounded annually. (a) What is the amount of the son's freshman year expense in terms of actual dollars (b) What is the equivalent single-sum amount at the present time for these college expenses"? (c) What is the equal amount in actual dollars the father must save each year until his son goes to college?

Answer 1

Future Value of money is a term used in economics to find out how a sum of money invested at a present time will become a particular amount of money in the future increasing at a certain interest rate for a particular period of time.

o Principle Amount (p)= $40,000 Time (n) = 4 years Inflation datel i) = 6.1 per year Market interat rate() = 8.1. Compounded annval year The freshman year = Loth So Amount of the son's freshman enpenes = plit into F = 40, of it sot $:712 633 Approx 16 Year Amount required Constant collare) Amount required (Actual Sallove) $40,00 71,633 tuo, Пло $40,00 $40,00 71633 1+i). geometric seres So we will pracht warth apply the Ofarmula

value of the moncy required in 9th year o = 71633 -liteln (178gth 716331-416o.or) 4 (1+0.08) $257, 994.63 Year-O Dallars) value of the amount needed ( Actual = $257,994.63 (P/f, 8 %, a) 257 994.63x0.50 $129,048.9. Aprex Yearly amount to be saved each year 129,048.91 (Alp, 81, 18) $19,228:29 Approx